Fractalis
by Jasie Song
Summary: SPOILERS if you haven't seen frozen don't read! When the kingdom of Arendelle receives the schocking news that it was Prince Han's twin brother Brinker, not Hans, who was behind the plot to kill Elsa and Anna, it sets off a chain of events that cause Anna, Elsa, Kristoff, Hans, and even the wicked prince Brinker to reflect on what true love is all about. K x Elsa, H x Anna, OCs
1. Dragon Curve

Fractalis

"Mmmm, Cocoa". Anna snuggled back into the loveseat and drank down the warm chocolate, watching her sister and Kristoff make ice-sculptures in the ballroom. Olaf and Sven were just goofing off.

Elsa had the unfair advantage, ice being her natural element, but Kristoff was surprisingly good at carving ice. Anna felt a bit of pride for her would-be suitor.

"You're cheating again." Kristoff complained as Elsa swept her arm to form a particularly delicate face for her scultpture. "We agreed to use the chisels!"

"I just can't" Elsa grinned, chiseling the collarbone and sending the frosty spray towards him. "The ice is alive, I want to dance with it."

Kristoff laughed, "No argument there." He left the statue of his ice-troll that he was carving to take the frozen hands of Elsa's ice-maiden. "May I have the first dance?"

Elsa giggled, waving her wrist, the sculpture coming alive to waltz clumsily with Kristoff across the icy floor.

"Don't forget me!" Anna jumped up, heading for Elsa, but was intercepted by Olaf along the way. The merry bunch skated and danced, having a wonderful summer's evening, until a loud knock at the door interrupted.

Elsa opened it, allowing the butler and a blast of warm air inside.

"Pardon me, your majesty, but a schooner from the Southern Isles has arrived in the Port".

"An official visit?" Elsa showed a trace of panic on her face.

"No," The butler bowed, "An urgent message. Pardon the presumption, but I thought you would wish to hear it immediately." He gestured, and a rain soaked man stepped into the room, shivering and breathing heavily. He must have ran from the dock.

Elsa immediately warmed the air around the shivering man as Anna raced over with a blanket and some cocoa.

"Yes, what is it?" Elsa coaxed him.

"Your majesties." The man coughed, holding the cocoa mug tight. "Firstly we must apologize for the actions -"

Elsa shook her head, "There is nothing you -"

"But there has been a terrible mix-up." The man interrupted. "The boat that arrived in our harbor, and the messenger carrying such a tale of woe, to think a prince of ours could have plotted such a thing - it was bearing Prince Brinker, not Prince Hans."

"Who - what?" Anna crinkled her forhead.

"Prince Brinker is the older twin of Prince Hans. He is in a similar situation, as twelfth in line to the throne. They both were present in Arendelle, both for the coronation and to strengthen trade relations with Weselton". The man took a long draft of cocoa, leaving his listeners in suspense. "Prince Brinker has confessed to conspiring with the Duke of Weselton. The two took advantage of Prince Han's situation as the fiancee' of Princess Anna and his position as temporary regent of Arendelle. Prince Brinker was to replace Prince Hans, which he did shortly after the Prince returned from the mountain with Queen Elsa. The Duke was to dispose of Elsa, though I am fortunate he failed in that endeavor."

"That's right." Elsa whispered. "Prince Han's saved my life. I thought later that it must have been an act, or that he purposefully aimed for the chandelier to try to kill me himself".

"So," Anna said slowly, "You are saying Hans didn't try to kill my sister? Or me? It was his brother?"

"Exactly." The man wrapped the blanket tighter. "Which brings me to why I am here. By Prince Brinker's account, he attacked his own brother and tossed him in the dungeon".

"But that was two weeks ago!" Anna's face blanched.

"Then we need to search for him." Kristoff offered, a lump in his throat.

"Immediately." Elsa agreed. "Send word to the guards," She ordered the butler. "We will scour the castle."


	2. Koch Snowflake

"Are you all right?" Elsa draped an arm over her sister's shoulder. "It's a lot to take in."

"I'm fine." Anna lifted the torch to get a better view of the lower halls. "At least, I think I'm fine. There was so much before that didn't make sense. Even if Hans was the world's greatest actor, there are some things you can't fake".

"Anna," Elsa warned, "It could still be a lie. A trick by the southern kingdoms. A plot to take over Arendell from within".

"It could be." Anna set her jaw. "If it is, you can send their balmy tropics to the depths of winter".

"Anna!" Elsa reproached her.

"Shh!" Anna froze, putting her ear up against the cold stone. "Do you hear that?"

"It's like a moaning," Elsa frowned, "Or a singing".

"But it's from above". Anna shook her head, "Hans would be below, if he is here at all. Why do we have such a large dungeon complex, anyway?"

"From the old wars, in the time of the sundering". Elsa sent a swirl of frost down the corridor to search out the air patterns, looking for any hidden openings. "The first kings were embroiled in endless wards. Arendell was built at the price of much blood and pain. Yet, the dungeon's have a good history as well. In times of siege, these walls protected the people, and not just our own. This island became an oasis, a refuge for all those who no longer had a place, who had lost their own homes to fire or their families to the sword".

"I never paid much attention in history". Anna shivered, wishing everyone had stayed together rather than splitting up to look. Still, perhaps it was better if Kristoff wasn't with her when they found Hans, even if she would have liked the moral support.

The frost flurries were acting up. "That way," Elsa gestured. Soon they could hear noises and shouts; apparently the guards had discovered something as well. The air grew cool and the floor rough as the two girls found themselves traipsing through rubble.

"This is near where I escaped," Elsa said quietly.

"Over here, your majesty". A guard called, "We found something."

Anna rushed over, Elsa on her heels.

The cell was blasted in, the walls and doors collapsed. There was dried blood on the floor, a knife that had seen a fight, and manacles on the floor. Someone had pried the manacles out of their anchor in the stone, perhaps with the bloodied knife. There were drag marks on the floor.

"Whoever was imprisoned here escaped majesties, but he would have been sore wounded," the guard informed them gravely.

"The cell," Elsa winced, "It must have been blasted when I made my escape."

"Then you probably freed Hans, too." Anna reassured her. "Can we track which way he went?"

"I think so." The guard nodded, holding the torch to the stony floor. "Follow me".

They spent a half hour slowly and painstakingly tracing the path through the winding and many layered dungeon. Finally, the tracks turned up, leading back towards the main castle.

"Wait". Elsa finally said, "I can feel him." She ran ahead of the group, returning a minute later to fling herself in her sister's arms. "I'm so sorry Anna! I'm so sorry!"

"What is it?" Anna reflexively hugged her sobbing sister tight. "What happened to Hans? Is he dead?"

"Worse," Elsa sobbed harder into her sister's shoulder, "I killed him".

Even with Elsa's confession, Anna was not prepared for the sight that greeted her. In a larger room, one of the guard stations, Han's had come to rest. He had never made it out of the labyrinth of cells back up to the castle proper. He had never made it back to her.

"Oh, Hans." Anna leaned down next to his frozen form and cried, stroking his icy hair. He was sitting at the guard's bench, leaning his chest over the table. He would look asleep, if his body was not a statue.

"I was so concerned with getting out of the castle," Elsa came to sit next to her, "I didn't know he was nearby. I must have struck him in the heart".

"And he froze here, all alone". Anna collapsed over his torso, "I think he might be the first person I met who was lonelier than I was. But I'm not lonely anymore, and he's gone. He should have never met me".

"Don't say that." Elsa petted her hair. "We would both be still alone in this castle if he hadn't. We owe him a debt."

"That I can't repay." Anna shivered, feeling the cold of his back through her clothes. He was ice, yet he was so cold that he did not melt. "We should move him somewhere nicer than this."

"The Hall of Heroes". Elsa agreed, referring to the castle's statuary hall, where all the great leader's and heroes of their people were commemorated.

"There's -" Anna sat up, startled, fingering a parchment on the table. "There's a letter. He wrote a letter. Elsa, he wrote me a letter!"


	3. Levy Tapestry

The letter was water damaged and stained with blood, and looked as if it had been written by a cramped hand. Anna's fingers ached just remembering the bitter cold that had froze her own, far deeper than frostbite or winter's nip, until they could no longer move.

* * *

"My dearest Anna,

I see I will not escape this dungeon, not in time for you. My wounds and the cold are against me, this unnatural cold that has pierced my heart. It spreads faster by the moment, robbing me of those precious seconds I would spend with you.

I do not blame your sister; she rescued me, in fact. I might have died in that dungeon if she had not escaped. My brother tricked me; he captured us both when I came to get his advice. He is in league with the Duke of Weselton. You may know this, but if you do not, be on your guard. My brother is not to be trusted, and neither is the Duke.

I am glad your sister got free, and I think my brother will find it more difficult than he thinks to take Arendelle.

I wanted to tell you good bye, and thank you, and I love you - there are so many things I want to say. It may be crazy, to love after such a short time, but I want you to know something my mother once taught me:

Love is a choice, not an emotion. You can choose to love a stranger, or your best friend. You can even choose to love your enemy, which has more power in stopping wars than any force of arms. I do not love you because I like you (though I certainly do), or because we have so much in common (though we certainly do), but because I choose to love you; for better, for worse.

This may be history's shortest love story, but I'm glad we shared it together. I pray you are reunited with your sister, and that the two of you rescue your kingdom together. If I am frozen, then I will watch over you - it may not be the life we planned, but it will not change my choice. I would love you, and love you again.

With warmest thoughts,

Hans"

* * *

"Oh, Elsa!" Anna hugged her sister. She didn't know what to think. All her feelings and thoughts for Hans had been flooding back ever since the messenger had come, and despite Hans letter, love certainly -felt- like an emotion to her. How could he be so dedicated, after knowing her only a day? She remembered the reports; he really had done wonderfully, running the kingdom; the people had loved him, before they thought he was evil and putting on an act.

Elsa consoled her sister as several more guards and Kristoff entered the room.

"Anna?" Kristoff rushed over, but Elsa warned him away with a flick of her hair. "Hans?" He instead turned to the ice-statue at the table.

"He was frozen," Elsa swallowed. "I froze him. I didn't know".

Kristoff looked at Elsa squarely, "There might still be a chance. Perhaps the trolls will know of something that can be done".


	4. The Mandelbrot Set

Kristoff shifted akwardly, feeling a bit out of place even though he was among his own 'family'. Sven nuzzled him, and his 'mother' troll, Bulda, patted his arm sympathetically. He had never officially met the prince; though he had seen the man (apparently, the twin brother from recent events) try to kill Elsa. He sulked, running a finger through his hair and dislodging his cap. Yes, he had told Anna not to make snap judgements, and he himself had only known her a couple of weeks; but he still felt like his claim was superior. He'd spent more time with Anna, he'd risked his life for her. What had this prince really done?

Kristoff sighed. He knew from his little experience with girls that this was something he would have to let Anna figure out, and that attempts to persuade her one way or another would probably backfire. So, he'd hung back; ready to give a hug or a comforting word if asked, but trying to be as out of the way as possible. That was as much for his own benefit as to spare Anna further confusion; he felt like a third wheel.

Up ahead, Anna and Elsa were entreating Pabbie, the troll king. Han's frozen body was propped up by a litter held by six guards.

"Bring him closer," Pabbie motioned, and the guards set the litter down. "Yes, yes, this is a problem. He's frozen stiff."

Kristoff rolled his eyes. Trust Pabbie to announce the obvious as if he was revealing great wisdom.

"Can anything be done?" Anna sniffled. "Are we too late?"

Pabbie knocked on the statue and listened, eventually crawling up Han's shoulder and muttering to himself, knocking on the back and head.

Another troll, Rockel, shook her grassy head, "It's never too late. But sometimes it's impossible."

"What does that even mean?" Anna scrinched her forehead.

"That there never has been a spell that could not be broken," Pabbie announced, climbing back down, "But that to break it is often far beyond what mortals can do".

Elsa looked mournful. "There is nothing we can do, then?"

"There may yet be." Pabbie picked at a barnacle on his cheek. "You see, he's not -completely- frozen. Place your head to his chest and listen closely."

Anna leaned over, placing her ear to the freezing cold.

"His- his - his heart~!" She jumped back, clutching her sister.

It was Pabbie's turn to look confused, "Somehow, his heart has not been completely frozen. A piece of it has remained untouched."

"How is that possible?" Elsa asked, "That is, that is a good thing, right?"

"Yes, yes." Pabbie muttered to himself.

Bulda stepped forward, patting Kristoff on the arm and leaving his side. "This is rare indeed". She listened against the chest. "He still lives; he must have a strong heart".

"Then you can help him?" Anna asked.

"I am afraid not dear." Pabbie shook his head.

"That does not mean that nothing can be done," Bulda interjected. "If his heart did not freeze, then he may be aware of the outside world on some level".

"Which means what?" Kristoff stepped forward. "What can we do?" While he was not pleased with the current turn of events, action suited him better than inaction. And despite his personal feelings, he wasn't about to let the guy die.

"Talk to him," Bulda suggested, "Any form of interaction, especially you Anna. He has the strongest connection with you." She shot an apologetic glance at Kristoff, who was shifting his feet sulkily.

"Left on his own, he might thaw eventually." Pabbie speculated. "But that might take hundreds of years. My daughter is right; the best way to melt him is to speak directly to his heart."

"I suppose I've talked to enough paintings to be used to one-sided conversations," Anna laughed nervously.

"Then we should take him back." Elsa ordered, "Put him in the library". The guards nodded and headed back. "Thank you, Chief Pabbie, for your aid once again." Anna and her bowed, while Bulda hugged Kristoff and Sven goodbye.

Kristoff hugged her back tightly. There was a weird pain in his chest and a confusing mix of feelings swirling in his head. Then Elsa tapped him on the shoulder, and it was time to return to Arendelle.


	5. Seirpinski's Gasket

Anna leaned back in her chair and kicked her feet, needing a break from the book she was reading aloud. "Oh, Hans," she muttered, leaning forward and supporting her chin with her fists, staring deeply into the eyes of the statue. "How long are you going to sit there?" Sometimes, she could almost imagine a spark behind those eyes, a hint of brown, but if she blinked it was gone. "It's been a week!"

Anna got up, moving over to the window of the library and peering down. The town was ice skating, as happened most Tuesdays now, with Elsa right in the middle laughing. Kristoff was down there too, somewhere, she could see Sven clumsily sliding on the ice while Olaf did circles around him.

"I don't suppose you want to go out and build a snowman?" Anna poked Han's in the forehead, he didn't budge. "What else can I do?" She pouted and flounced back onto the chair to finish the book.

* * *

"Can't catch meeee!" Olaf did a pirouette and then skated off past Sven. The reindeer snorted and chased after, two little kids perched precariously on his back.

"Sven's sure popular," Elsa skated up to Kristoff.

"That's because he's the best reindeer in the world," Kristoff stated proudly. "I wouldn't know what to do without him, he's never let me down".

"At some point you have to trust people, too." Elsa looked at him squarely. "Take my hand".

"Oo-kaay," Kristoff reached out, and Elsa took his hand firmly.

"Stay with me". Her grin was impish as she waved her other hand, and ice began to form in mounds circling the ice rink. When she was done, the ice dipped and rose in a path. Elsa skated with Kristoff in tow to an ice ramp up to the higher level. "Wohoo!" She whooped and began to slide forward, the two climbing up the first hill as if on invisible tracks.

"What is this?" Kristoff barely had time to ask before the two plunged down the first drop. It was only eight feet, but it was exhilirating.

"Don't let go," Elsa grinned and the two picked up speed. Swirls of her ice crystals were still working in the air, forming little ice carts that people could sit inside. Several of the children were quick to explore, and were soon laughing happily as the magic carts slid up and down the ice.

"Wouldn't dream of it", Kristoff stared at the drop off beside him. If they lost their balance -

"Just enjoy it," Elsa turned in towards him, herself skating backwards so she could look at him. "Trust the ice".

He grinned and let himself give in to the rush of the air as they plunged down another dip down. At points, it felt like flying. Kristoff felt a pang in his chest as the two past the castle. Anna was inside, she'd been inside for a week.

He'd visited her a couple times, but she could never spare long, and he could tell a heavy weight was on her mind. He wished she could be outside too with Elsa and him, enjoying Elsa's weekly fake winter that she held in the town square.

* * *

"As the moonlight caressed the garden flowers, the two of them kissed, binding their fortune and their futures to each other." Anna shut the book, "The End".

She looked at her icy-fiancee. She had started thinking of him as her fiancee again in the past few days. He had made a commitment to her, even if she certainly planned to have a discussion about that if he woke up. _'When he wakes up'_, she chided her brain for being negative. "Did you like the book?" Anna asked the air. "Fortune and future", she mused, "That is a strong commitment. For better or for worse, they are tied to each other, as if the other was their own self".

She thought she saw a shimmer of light under the ice for a moment, but then the butler entered carrying a candelabra and she realized it must be the reflections of the flames. Han's remained still.

"Your highness", the butler bowed, "A ship from the Southern Isles has docked. You asked to be informed as soon as they entered port. Do you wish messengers sent?"

"Yes," Anna nodded, "Send them welcome and an invitation to stay at the castle."

"Immediately," The butler left her to her own thoughts.

Anna idly stroked Han's cheek, her most recent way of fidgeting. "I have a plan, I do", she encouraged him. "I just need to find out more about you".

A snatch of melody drifted down from above. "There's that singing again", Anna looked up at the ceiling. "I wonder if it's one of the servants? Do you think so Hans?" She tried to force a laugh, "Oh do stop talking so much Hans, my ears are tired"! She weakly climbed onto the cushions where he was propped up, leaning her head onto his shoulder. "Please wake up. I need you to be here".


End file.
